304 Index
Multiple risk models , 23
discussion and conclusions , 34 – 5
fundamental and statistical risk model,
constraining active risk with , 27
portfolio construction using , 25
out-of-sample results , 33 – 4
second-risk model constraint , 32 – 3
Multisolution generation , 23
constraint bounds , 36 – 8
constraint elasticity , 39 – 41
constraint modifi cation , 36
intractable metrics , 41 – 51
N
Neumann – Morgenstern expected utility
theory , 74
Non-Gaussianity, importance , 268 – 70
Normal distribution , 251
Normal Inverse Gaussian , 256 , 275
NUOPT ™ , 287
O
Omega, and GLO , 67 – 8
Omega ratio , 203
Optimal mean/downside risk frontiers,
computing , 179
ellipticity, role of , 179
case of two assets , 184 – 90
conic results , 190 – 4
main proposition , 180 – 4
simulation methodology , 194 – 8
Optimal portfolio (P0) , 24 , 36 , 43 , 46 , 86
Optimal weights, computation of , 151 ,
294
Optimized hedging , 56
P
Parametric optimization, of WPA , 111
Pearson Type IV , 256
Performance ratios , 132 – 4
Portfolio attributes, of WPA , 112
effi cient surface , 112
higher moments , 112
joint probability of loss , 112
probability of loss , 112
value at risk , 112
Portfolio construction, novel approaches to:
multisolution generation , 35
constraint bounds , 36 – 8
constraint elasticity , 39 – 41
constraint modifi cation , 36
intractable metrics , 41 – 51
using multiple risk models , 25
discussion and conclusions , 34 – 5
fundamental and statistical risk
model, constraining active risk
with , 27
out-of-sample results , 33 – 4
second-risk model constraint,
constraining specifi c risk as , 32 – 3
statistical risk model, constraining
total risk predicted by , 31 – 2
Portfolio dimensional problem , 121 – 5
Portfolio managers (PMs) , 6 , 24
Portfolio optimization , 37
active quant management , 56
algorithm , 257 – 61
applications , 55
asset allocation , 56
history , 248 – 51
index tracking , 56
long – short portfolio construction , 55 – 6
need for , 55
program trading , 55
with threshold accepting , 201
algorithm , 210 – 11
diagnostics , 218 – 20
implementation , 211 – 15
portfolio optimization problems ,
204 – 9
stochastics , 215 – 17
see also Heuristic portfolio
optimization ; Second-order cone
programming (SOCP)
Portfolio selection, optimization and , 161
auxiliary parameters , 174
basic statistics:
continuous version , 172
discrete version , 171 – 2
downside and upside statistics, analytic
expression for , 175
DTR ™ optimizer , 167 – 70 , 171
Forsey-Sortino Optimizer , 162
basic assumptions , 162 – 5
optimize or measure performance ,
165 – 6
lognormal cumulative distribution
function, formula for , 174 – 5